How do you find f'(x) using the definition of a derivative for f(x)=e^x ?

1 Answer

Refer to explanation

Explanation:

The definition of the first derivative is

f'(x)=lim_(h->0) (f(x+h)-f(x))/(h)

hence for f(x)=e^x we have that

f'(x)=lim_(h->0) (e^(x+h)-e^x)/h=lim_(h->0) e^x*((e^h-1)/h)= e^x*lim_(h->0)((e^h-1)/h)=e^x

Remarks

lim_(h->0) ((e^h-1)/h)=1